Simplified method in polynucleotide helix-coil transition theory including binding of complementary monomer

The grand partition function for a long linear system of alternating alpha and beta sequences with the restraint of a fixed number, N(alphabeta), of alphabeta boundaries depends in an extremely simple way on the alpha-sequence and beta-sequence grand partition functions, xi(alpha) and xi(beta). When the restraint is removed, we have mualphabeta = 0, where mualphabeta is the chemical potential conjugate to N(alphabeta). The grand partition function and the condition mualphabeta = 0 lead to the fundamental relation 1 = xi(alpha)xi(betaz2), where z = e(-omega)alphabeta(/kappaT) and omegaalphabeta = boundary free energy. This is a generalization of an earlier equation of Hill, and is equivalent to a result due to Lifson. Binding of a substrate does not affect the argument: the new component is simply included in xialpha and xibeta. A model for the binding of adenosine on poly(U) is used as an example.